We consider a nonlinear elliptic equation driven by the sum of a $p$--Laplacian and a $q$--Laplacian where $1<q\leq2\leq p<\infty$ with a $(p-1)$--superlinear Carath\'eodory reaction term which doesn't satisfy the usual Ambrosetti--Rabinowitz condition. Using variational methods based on critical point theory together with techniques from Morse theory, we show that the problem has at leat three nontrivial solutions; among them one is positive and one is negative.
Wang’s multiplicity result for superlinear $(p,q)$–equations without the Ambrosetti–Rabinowitz condition
MUGNAI, Dimitri;
2014
Abstract
We consider a nonlinear elliptic equation driven by the sum of a $p$--Laplacian and a $q$--Laplacian where $1File in questo prodotto:
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